{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## PS1-5 Locally weighted linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### (a)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "##### i."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Recall the cost function\n",
    "\n",
    "\\begin{align*}\n",
    "J(\\theta) & = \\frac{1}{2} \\sum_{i = 1}^{m} w^{(i)} \\big( \\theta^T x^{(i)} - y^{(i)} \\big)^2 \\\\\n",
    "          & = (X \\theta - y)^T W (X \\theta - y)\n",
    "\\end{align*}\n",
    "\n",
    "Notice that there are only $m$ $w^{(i)}$'s, and $w^{(i)}$ only takes effect on the $i$-th entry of $(X \\theta - y)^T$ and $(X \\theta - y)$.\n",
    "Hence, $W$ is a diagonal matrix, and the above equation holds by picking:\n",
    "\n",
    "\\begin{equation}\n",
    "X = \\begin{bmatrix}\n",
    "     - (x^{(1)})^T - \\\\\n",
    "     \\vdots \\\\\n",
    "     - (x^{(m)})^T - \\\\\n",
    "     \\end{bmatrix}\n",
    "     \\in \\mathbb{R}^{m \\times n}\n",
    "\\qquad\n",
    "y = \\begin{bmatrix}\n",
    "     y^{(1)} \\\\\n",
    "     \\vdots \\\\\n",
    "     y^{(m)} \\\\\n",
    "     \\end{bmatrix}\n",
    "\\qquad\n",
    "W = \\frac{1}{2} \\mathrm{diag} (w^{(i)}, \\dots , w^{(m)})\n",
    "\\end{equation}"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "##### ii."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "To simplify the calculation, let $J(\\theta) = \\frac{1}{2} (X \\theta - y)^T W (X \\theta - y)$. To minimize $J$, take derivative w.r.t $\\theta$ and set to 0:\n",
    "\n",
    "\\begin{align*}\n",
    "\\nabla_\\theta J(\\theta) & = \\nabla_\\theta \\big( \\frac{1}{2} (X \\theta - y)^T W (X \\theta - y) \\big) \\\\\n",
    "                        & = \\frac{1}{2} \\nabla_\\theta (\\theta^T X^T W X \\theta - 2 y^T W X \\theta + y^T W y) \\\\\n",
    "                        & = \\frac{1}{2} \\nabla_\\theta \\big( \\theta^T (X^T W X) \\theta - 2 (X^T W^T y)^T \\theta \\big) \\\\\n",
    "                        & = \\frac{1}{2} (2 X^T W X \\theta - 2 X^T W^T y) \\\\\n",
    "                        & = X^T W X \\theta - X^T W^T y \\\\\n",
    "                        & = X^T W X \\theta - X^T W y \\\\\n",
    "                        & = 0\n",
    "\\end{align*}\n",
    "\n",
    "By solving the equation, we obtain:\n",
    "\n",
    "$$\\theta = (X^T W X)^{-1} X^T W y$$"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "##### iii."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "\\begin{align*}\n",
    "\\ell (\\theta) & = \\sum_{i = 1}^{m} \\log \\frac{1}{\\sqrt{2 \\pi} \\sigma^{(i)}} \\exp \\big( - \\frac{(y^{(i)} - \\theta^T x^{(i)})^2}{2 (\\sigma^{(i)})^2} \\big) \\\\\n",
    "              & = - m \\log \\sqrt{2 \\pi} \\sigma^{(i)} - \\sum_{i = 1}^{m} \\frac{(y^{(i)} - \\theta^T x^{(i)})^2}{2 (\\sigma^{(i)})^2} \\\\\n",
    "              & = - \\frac{1}{2} \\sum_{i = 1}^{m} \\frac{1}{(\\sigma^{(i)})^2} (\\theta^T x^{(i)} - y^{(i)})^2 - m \\log \\sqrt{2 \\pi} \\sigma^{(i)}\n",
    "\\end{align*}\n",
    "\n",
    "Thus, maximizing $\\ell (\\theta)$ is equivalent to minimizing\n",
    "\n",
    "$$\\frac{1}{2} \\sum_{i = 1}^{m} \\frac{1}{(\\sigma^{(i)})^2} (\\theta^T x^{(i)} - y^{(i)})^2$$\n",
    "\n",
    "By setting $w^{(i)} = 1 / (\\sigma^{(i)})^2$, finding the maximum likelihood estimate of $\\theta$ reduces to minimizing $J(\\theta)$."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### (b)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "outputs": [],
   "source": [
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import problem_set_1.src.util as util\n",
    "\n",
    "from problem_set_1.src.linear_model import LinearModel"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% code\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "outputs": [],
   "source": [
    "x_train, y_train = util.load_dataset('data/ds5_train.csv', add_intercept=True)\n",
    "x_valid, y_valid = util.load_dataset('data/ds5_valid.csv', add_intercept=True)\n",
    "x_test, y_test = util.load_dataset('data/ds5_test.csv', add_intercept=True)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% code\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Take a look at the training set:"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "outputs": [
    {
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0x22aab548dc0>]"
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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gdqtQEcY2wmshPAoJ4cjS5qGfZ3adqtOntT5xIq4y9hVf4iTntY0khp5yQk85//MNAGfmnTuEUEhHandmKVsyWQaDWS9pPG5nHCbkGIXsOx1LvN8WTDFKpGyxhspcELuX4KuOShuTfkV2YOxb6OkYgK8DuNsazH515jPfg+mkwAcA/K4cl71S248i9oYghAg9XbgwtZiF0ci875obN6a7ugnb2zqqHe/sMTB5DlJGn2G5vi51X3epG5dtQzxH2Z5XRKNXQmHKhYcAfOUg++ldB+89CuDRg9/fAeDLByLyaQB/pcp5fQlFUaW5cKFZI0ppAK7twey2701eiMfeuyIkYmHaY2BteT3j8XTAXI5lwLxNsWjbc6pT/1y3DYaePL98CYXPTiv2bButwzfWtr53PNb65Emtl5amHXKbYzJFZTpzZnYfa7Ew7QFsn/dH9hjf2jqcXdWGWISaG1Gl/vmqo70fzPb58hl68vngYp4kFNrraePe2B7jffdNO0V5P+TcmDxvdjA4XB7f4aCtLXNf7r233RTc0IZUWf3zOUbR+/RYny/fYxQ+Oq3QDWEeMcSofd8bO5xy5sy0UxQLOrZn0jZyf+69d1Ys2hKJUEbKvPrnO+vJ9XmLoFA4xNegVcxjFDGIRFv3JhvzF7Gw51SEuh8xPAcRURGLrS3/3x3DdcfaNl1CoXCEr0oTe9ZTyMbi894UhXMk7CRisb09O9M+1P0I/RyyM75FRLNZaV0i9rbpEgqFA/JSJ8dj814XK02W2ENji5DX8coA8bwJd23dj2xHJYPqm5vtPwdbLOR7ZfmQLtSHvkOhcECfXNAiYh5sXxS7w7fz1PM6xawl2cb9yKt39goAbdMnC7tvUCgc0UWruipdvnbp8Dc3q3eCbdyPvFWJV1ZM6m4XnwMJC4XCIV20qufRZW9qkYyW0cgsxOf7fozH00luUu8ArYfDduZN5EGPortQKBzRBat6kYbe1c6higDmfcaeoWx/zsf9kCysEye0Pn7cTALMLs7Y5nPostHQdygUDuhKA+nKdbgg5Do+VRmPjUjIznW+F4arWqbUDaZ5dNU4KoNC4YAuVJy8mHfIZSlSIlTIUVYllu1Nt7fjqHddD8H20aCiUBCt9Wxll4a+vNztyu+CUBa0fK9kX2VTdkPRB49C6/5cp0Ch6AguvBqZK7CyEs+qqDETyyQ3ec7D4eGBdI5R+KPrnpNNmVAcAUmGtTXg0iVgMjHHk4k5Xlurd55nnwX+/M+Bd74T+PCHZ89ZxM2bhz8zmZj3u8zeHrC7C2xsmOONDXO8t+f/uy9fNs9Kvn9tDfjQh4Br18z3L/r8m9DW/Yihvk0mwK1bwM6O+TmvjXSaIgVJ+dVVj0Lr5u6w7FRXdye+vlmSsdKXcEjT+tbU++5jfQdDT91iUXe4aeXvSycVK21vZBOaJvUttNCkCIWiQzRpPE0r/40bh7fd7HrjiYnxuN2tMfNoswNtWt9o2NSjTCg4RpEQEpPe3TVx6t3dauMLwuXL09i2ILHvKrHfY8eAD3wA2N42MdvHH28/Rt43srF6rYHnngM+9SlAKXPcJq7GyarQtL5tbADDIXD9uvkp4ypkAYoUJOVXVz0KV1lPi7jksaZqdh37+UgWlL0oYAiPrg1LXcbS7PoGaP3ww3GVs0uAoSdis0gDskVKYuTb2ww7+aBsaXEJN4Xu/HynjcpEQ3tMZmmp+uTQPg5GN4VCQQ7RdEA8dEeVCot4gWJN252cLONRtoFSW8j3inBlRc2V8SACubxsrrvO0iV9HIxuCoWCzLBoZ08rrT517pm9xIoMWm9vm8UAlTI77/nsmKtgl98upxy7rA/j8eEwG+ubPygU5A5NOntaaYtRVZjlc4OBic0vLekolha3ye70KGLxmte43+lOwk915/yQxaBQdAQXHTU7+8Voet+qhvqk47VF4siRw8t2hNyCNytWMtC8ve3vO0ILZB+gUHQENp5wLBJCsv/31Knq+1xLxytLi8vvRft3h0DKINlv29vuytT3/elDQaHoCPYiceKOj0ZsPG1RNRSSjePbE+PmdfLjsdnqdGlp6lVsbxuPIrYtULOehCsBo0EUBgpFR7CtOGmgbTagvoet6gyu2plB2dnTRfcsO0Yhq/zKfILNTb1QppoPxmMjXtk66Ko+MLuufSgUHUK2xlxfb3/CW98tvbrpmvZ8k+x58jrT7MZS8ruky8Ywf0Lr9upBn5b4jgEKRUcI7VHYZYihw2oTuzOUDiwvyyfb2UsM/+LFw+fJ/o99fPHidHKZCNTFi/FkPo3HWl+4MDtuIqHRCxeaf0foetZH75lC0RFiGaPoo6UnHYc9TnHqlDmWl9bTMYnV1emA7Opq+YBvnoVuz0/IbmAknwndaYl3K2KRPV4Ue1a21tP70eaWvX30nikULeLTEomh8oa29EKS7cDleGVl2rHduKH1a19rWpZMkBuNzDwDwPzMdngiQNn7msK99hEKzZuZLqLcJincf5dQKFrEZ2ce2h2OQahCkg0riVfxwAOHF0u8/359Z32i1dXpLGulDs+JyIa0bE8tBe9NUnjX192dM5ZOOoX77woKRcvEUsldE1qoYiK7edDqqtZbW+Y9EYm779Z35kBI2EmymfLSbOlRzBK6kw59/9tubxSKAISu5MQfeR3IcDgrDj/wA+bnK14xnQ9hb77z8pfPCo2IiAwQZ0NcEpqKSSx8jVFoHb6TjsF7brsM0QoFgAcBPA3gGQCP5fxdAfjlg79/AcB9Vc4bWih8VvImVgY9gubkNV7xEMSjuOsu83Nrazqwbc/KttNsZZBWQlfyU7KesqmyMT0rO+tJcJH1FEMnHUtbaVMwGwkFgHcAeMG8z9V9ATgK4GsAXgbgBICnALwq85mHADxxIBivBfCZKufu6hhF0/PH0ABTJ68DGQxMx766OvUo7r/fvL+6ajwKWyBsT8GeVJd9LjGHnHwSSycdC21FJ5oKxS8cWPS7Bx6Amvc/VV4AXgfgSev4CoArmc/8GoC3W8dPA7hr3rm7mvVkn2/RjqTvnZAPZIziDW+YioRSWt9zj1l2w05htlNptZ52Apubs+dk6JJonZBHoachoJ8A8MED0fgHAF5e5X9LzvkWAO+3jrcBvCfzmY8C+BHr+JMAzhecbwBgH8D+2bNnfd3LaGjSkbATcsuNG2aMQinz88yZ6YD2cFj8f0WdQN/FnB6FIaYxiiMV99XWAP7g4PUsgBcA+JdKqZtV/r8AlfdVC3xGyvg+rfV5rfX5F77whQ2KFT+TidlsfmfH/JSN7n3/L8nn8mXg3Dngl34J+NCHgHvuAW7fBra2zPt5TCbApUvA7i5w7Rrw5jcDjzwCPP749P2NDfP+pUv9ek5ra7PXLPdqbS1sudpmb29aDwDzc3fXvN86RQqip5b6zwK4DeBJAG8FcPzg/SMAvjbv/0vO28nQk284RhE3srzK+nr5vS3aF/uBB2ZTY2McxG6DvntVIUDDMYprAL6v4G/3zPv/kvMeA/B1AHdjOpj96sxnHsbsYPZnq5y7y0LBrKd4kfRQe0Z2nc6eneMsDJG2SyOh8PmCyWr6Ckz207sO3nsUwKMHvysA7z34+xdRMD6RfXVZKEicjMcme2k0ms1uGo2m2U+SSmrP8BbxkN/rrjgbAz4MEIpm+0QrFL5eFArSNkWhpFe84rB3IfthZzczyi4DEtOOdmW4DmmGDJH22eumUBASgOxy5Pa8CVn/yV4F2O4MJYwVYin5RXDpAYTsrPs8jkehIKRl7I7TXttpZUXfibvbMfi8zlEGxlOJ0XdlTKGvYS8KBXFKn93zKuRZpbKF6vKy6YBkDKOoM0qts0qtvPPoiujVoUwoKs2jIMSGee7lZPPfAeDIEeDYMeDECeD5zzdryio1zY3Pu58yxyL799hIrbzz4FyjHIoUJOUXPQr/dM2C9IXcJ1ngT5b7kOyobNaT1ul5bDduTK9PGI/Ne7GWuQiOUTD0RBzTR/e8Lql1+ovSlQ62L88rjzKhUObv3eL8+fN6f38/dDE6jYQbhkPjnmdDLaR/sE6kjVLqttb6fN7fOEZBatO1mDRxw8aGEYnr181PisRhbt483E4mE/N+zFAoSG2iWqyMRAMHgeeTaiIIhWIOqVoAhLQJvcxq2FluV6/OrhQcMxSKOaRqAfiE94Rk6ZKX6ds4TDJEVzTKnfLLddYTU0EPw3tCuorvDK5Y2w6YHtucmFJBY0nhi+meEOISX515zGnEZULB0FMFYhukWyT049qdju2eEOISX+GhZEN0RQqS8sulRxGrBVDX4nF5HbHeE5I+sXjLsYaHfAKGnhYnloqbR93Qj6vKH/M9IWkTgxESQxlCQKHoIIt2+hxXILET2ppf1BBK3YCiUHSMRS2e0A2QkHlIZ2sbNKl0tql7IhSKjrGI5ZJ6JSb9QHYBlI2eZN+OVOppFWMsVs+jTCiY9ZQgly8fzsLY2DDvF+Ey24Kz1Yngoy4oZfbrAKb7dqRClWypJCesFilIyq+uexShoXdCBNd1IeXQk9bVw7sxhoHB0BNxTYwVnYTBdV1ItW7VFc3YEksoFMQLsVV0Eg5XdSFlb7XO2EOMYkihIM6JsaKTMLisC7EO9LokVjGkUBCnxFrRSfuwLtTHtRi6Ol+ZUDDridQm2fVqiHO6VBfayuarm7U4r1ytZFEVKUjKL3oUhBCtFxs3iM07qlIuF+E/MPQUF32IwxJSB19tom7nH+vYW5VyNU0ooFC0zLxKH6vlQkgofLaJwWA601vOWSZCsWbzlZWLHkWCQtGWq0hIl/DVJsZjrZeX9cwEvqLzx9ouy8rlSmQpFAFow1UkpGv4aBPjsfEolpe1XlkpXjsqVk9/XrnayHoK3qn7eMWyH4VvV5GQLiBtzG4Tp06ZkFFT7E5V2uPKSn57i3XssK1yUSgasKiVMc9VXFnRejSa/exoFL5SEtI2YvGLpZ89boJPESr7PpsYxKYK0QkFgO8G8HEAXz34+YKCz30DwBcBfL7sIrIv16GnutZ/FVdxNJp9bzTSenWVngXpJ3UHnOvQZkgp1vBVFWIUipsAHjv4/TEANwo+9w0AZ+qe38cYRZ3YaVWrIvXwU8rWE4kPX2N2bdfTVNt1jELxNIC7Dn6/C8DTBZ+LQih8PviUB7RTtp5IXKTauRaRYruOUSj+JHP8vwo+918AfA7AbQCDquePYYyizrlTbhxduAYSlq4ZHKm2iSBCAeATAL6U83pjDaF48cHPvwDgKQA/WvJ9AwD7APbPnj3r7ObFMmM0ZlK0nkg8dCmE6aNd9zbrqWroKfM/fx/AO6ucP4Z5FPPoSuNI1XoixAc+2nVbRmWMQvHuzGD2zZzPrAL4Luv3TwF4sMr56wpFVzrttumSV0RIzLRhkJUJRahlxv8hgC2l1FcBbB0cQyn1YqXUbx585kUA/qNS6ikAnwXwMa31b/koTJKbnUfAu98NXLkyu8T0lSvmfUJSoq0lxhdlYwMYDoHr183P7DLl3ilSkJRfi4SeGEKpDz0K0hVir8t99SiiI7hiJ4ZYWru7xvu6ehV405uAN7+Z946kx96e8YalLl+6ZI7rbsDkwzORCMfuLnDt2rTNZb/HJxSKAyYT4NYtYGfH/GzzIfjEl0st4TpgKrDf/jbwtrc1Oy8hIVhbA37xF4ELF0xdvnDBHNcNP/sIY0exi2CRq5Hyq27oKXa3swm+54GcOmXWrVpeNkswdOGekX4yGmmtlNbr6+anrMVWl6IwUexJM4gt68n3q09ZT1XK7iu+OR5rffy4PrTOPxc3JKkhdXd729Tn7e1mbSVvblHsBimFosNUrXw+JsUNBsabsNf4H42Kl3EmJFbshTrFoFrU4CkzzGJOmqFQBKBNL2Ve5fNROW1BGo+nG8OUhZ9S9txIt3Fl7Vc5T6wrGVAoAtC2m1lU+XyVI9vpy/dvbhb/z3hsllLnPhzdJVVjwFW5X/lKrYfD2feGQ/O+nHNRoy2vjIPB4b01Fr3fFIo5+F7PybebWfY9bTTcOtcpA4YSA87uy0HSRurCYDD1Nl3vLxEzUr/FGLKPmxptef9/6tSsF9/EEKRQzMGH1S0dtG3p+2gog8HsTmBSeXzt4JVlkXsnA4br6xSJLmJnw9m71oV81m16OkXZUy7KkGeUuTJIKRQVcG3922q/s+Nua8cssjOY3VGfPt2eUNSt/HKf19f1newS0j3s/aljGLhtOxQs9Xt93f2588LMLsY9KBQVcTnIJB32qVPTfXp9zTOIOZPCxh6TkFTEJvnqJE7s+ri87K5NuSyXz3biaj5GHvY1yHif/V4TI5FCUQHXlait0JOQJ3KxDSwW7RXOdNrusEg2XJv4zjgqG6NoStYLGo3MtayuTu93E4OUQjEHX25p6MHstt3tKsQmXsQt8nyzgjEYhK97bbTHCxcOi8JoZN5vSl7befhhrZeWDo9ZMOvJg1CkvNnIvO9JJSxFusWNG9PMJ0EEI4RRMB4bz7WLqdmuvCQKxQI0FY+2LOcq3xPLBB96E/0iJo+2KOwpYZtUcWkIUigWIKZK3oSYPIqu3FNSnZjqX4zlaYLr9kShWJDUK1WMHXPq95TUJxaPVoitPIvi2kOnUFSg6KZvbqZbqdoO9VT9vq40VDKf2AyD2MoTExSKCuRZ3/Y8CFaq+VTxYNhQ+0OV+hBi8cy2POzUxuQoFBWxO7HsTGpXlSq1ylOXMiGIMRRG/FFnr5Q26kTbbS+1+k6hqIG9CqqPSpVa5VmEotBS10WSLPaMu+hlZueTyOoMbS2tswgUior4qLB5DUdmI3epYQhdbPSkOnUNobZXMGgL+7rtda+atAffhhaFogK+LP2i88oKql0a0O2Dt0TmU8dYyI4F+lwTrW3GY61PntT6xInDK+k22TnPV/sqE4ojIACAvT1gdxfY2DDHGxvmeG+v2XnlPJcuAVevmp9XrgBPPAHs7AC3bgGTSfPyx4Cve0jSYmMD+KEfAq5fB4bDaX2YTICbNw9/XmtAKfO7Uua4K3znO8C3vw381E8BH/kI8MgjwJveBKyt1T9XXl9itzevFClIyq8YdrjLIu5ndtN2Wt2ka4zH0/0olpYOb9pjW9RdDD3JNckWALJK8mte02x1V9/3Cgw9hcEe0FpZMRXlxAmtL140f5fKFGr9G1/43rKRxEtWEFZX9aEVTrueMi1CKSG08di0+6b7r9jn9bHHDYUiEPaDlXVlpNGMRv42MwpNXizV5ZaNJF6K9lI/frxfKdOy86Q97rK93WxA2/d4DoWiJi6zC7IVZnXVWBfHj3dTJIQ8K7FrliMpx37eKyv6TrjEbl+21y3tqyueZl62UxMhzIaetrfd3jcKRU1cWzl2TFF+95XxFNNcBV9bNpL4yYag7D20s6u4dsWLsJFr2tw8bBA2aY921qS9IZKLe0ihWABX1m92ws3qqtnxy06Xc0loVz5vopEM4NGj6A/zNjASsQhdF1LaiyZ7Htk9L5sgsygUigVpav0WDexJFoivMYqQHbJYjydPTq9TBHJ1dTqg3UUrkhymrCOOwbv00alnr1n2wsguXVJXjPLupcv5WBSKBXDR2WZjsYPBbIURC8tHWChkIxwMpp6TDLbJlo2uXHCSDkWrE6yuhvcotPZvWPn2MFyVm0JRk9Dhm6bEEOIRoVpejqMzIOEoCpm4jK83xadhZe+uJ22hyRasRbv1NV0ihEJRk5gGhOsSg8jlZbtk88dTuZ/EDdk6ISJh/z1UfWjLo5AwUdMxBQlju97/OzqhAPBWAF8G8B0A50s+9yCApwE8A+CxquePZR6F1mE2Dwq5qX1etsvSUnwWJGmfGMYksrRlWIkXtb4+2xYWxYe4xSgU9wB4JYB/XyQUAI4C+BqAlwE4AeApAK+qcv6YhCKEhR/Sq7CXL7AXQbt40TSQ++6jSPSRGMKhebRhyLn2KATXwhudUNz58nKheB2AJ63jKwCuVDlvTEKhdZhGErJh3rhhhMGeNToaaX30aHwWJfFPDOHQkLgeo9C6Jx7FnS8vF4q3AHi/dbwN4D0l5xoA2Aewf/bs2eZ3zTG+3W7fqXN1sGOmtiUVS5YLaZeUx/yaUjTwLGtfLYIv4Q0iFAA+AeBLOa83Wp8pE4q35gjFr1T57j56FL4n4yxannPnTC2zU2ObNhRCUmE8nh28dzHw7Et4U/UoOhF6sjvwPOvCpWVlx0JjGDwWT+LIkWnqnqsMDZImffQuYh2fyZKqUBwD8HUAd1uD2a+uct4mQuG6Itvny3aSPjpwe8Ewm7Ybo+3R2EuXdGX3MrIYfRqvsNu+3S5jFcXohALAmwB8E8C3APx38RwAvBjAb1qfewjAVw6yn95V9fxNhMJ3RfZpXcRiueS528vLprZtboYpE4mHWOqpb/LG6lykxvoiOqHw/WrqUbjOUMjiY2A7Jkst65WNx8aT2NzsdsdAqhPjnAofjEbmOre2ZkUjxtArhaIGvnKes+d3bU3FFvudt3ooxaK/9MWj0Nq0g60tPRMOjjWZg0JRE9ezKIWYrH7fyLXJLPGsYMRmTZF26FMb0PpwgkmoLMQqUChq4NOj8Gn1x+ZRyPf3xXIk1YixnvoiK4J2nxIjFIoatDFG4YNYLbW+xKIJyZKX8bi9HWfYSWsKRS1i7XCrEJsFH1t5SFj65E3YpNKnlAnFEZAZ9vaA3V1gY8Mcb2yY4729sOWqwsYGMBwC16+bn3INIZhMgEuXzL27ds38vHTJvE/6ydrabB2QOrK2FrZcvkm5TxGUEZJucf78eb2/vx+6GK0jDW84BG7dmq2cbXPzpukA7O+fTEzjuHw5TJlIeGKqo2QWpdRtrfX53L9RKLqBbcFvbBw+JiQWrl41Xu/OjvE2SRyUCQVDTx2hC+4t6T6TifEkdnbMT4Yi04AeBSGkFej1xg09CkJIcOj1pgs9CkIIIfQoCCGELA6FghBCSCkUCkIIIaVQKAghhJRCoSCEEFJKJ7OelFJ/BOB3QpejBmcA/HHoQrRMH68Z6Od185rT4Pu01i/M+0MnhSI1lFL7RWlpXaWP1wz087p5zenD0BMhhJBSKBSEEEJKoVDEwftCFyAAfbxmoJ/XzWtOHI5REEIIKYUeBSGEkFIoFIQQQkqhUESGUuqdSimtlDoTuiy+UUq9Wyn1n5VSX1BKfVgp9fzQZfKFUupBpdTTSqlnlFKPhS6Pb5RSL1VKTZRSv62U+rJS6udCl6ktlFJHlVL/SSn10dBlcQWFIiKUUi8FsAXgd0OXpSU+DuAHtdZ/CcBXAFwJXB4vKKWOAngvgAsAXgXg7UqpV4UtlXeeBfB3tdb3AHgtgL/Tg2sWfg7Ab4cuhEsoFHHxjwBcBtCLDAOt9b/TWj97cPhpAC8JWR6PPADgGa3117XW3wbwQQBvDFwmr2itf19r/bmD3/8UpuP83rCl8o9S6iUAHgbw/tBlcQmFIhKUUm8A8Hta66dClyUQfxvAE6EL4YnvBfBfreNvogedpqCUOgfgNQA+E7gobfCPYYy97wQuh1OOhS5An1BKfQLA9+T86V0A/h6AH2+3RP4pu2at9b85+My7YEIVv95m2VpE5bzXC69RKfU8AP8KwM9rrf9P6PL4RCl1EcAfaq1vK6VeH7g4TqFQtIjW+q/lva+UuhfA3QCeUkoBJgTzOaXUA1rrP2ixiM4pumZBKfW3AFwEsKm7O6nnmwBeah2/BMB/C1SW1lBKHYcRiV/XWv/r0OVpgR8G8Aal1EMATgI4pZT6gNb6bwQuV2M44S5ClFLfAHBea53a6pO1UEo9COBxAH9Va/1HocvjC6XUMZjB+k0AvwdgD8Bf11p/OWjBPKKMxfNPAfxPrfXPBy5O6xx4FO/UWl8MXBQncIyChOQ9AL4LwMeVUp9XSv1q6AL54GDA/h0AnoQZ1N3tskgc8MMAtgH82MGz/fyBpU0ShB4FIYSQUuhREEIIKYVCQQghpBQKBSGEkFIoFIQQQkqhUBBCCCmFQkEIIaQUCgUhgVBK/ZZS6k+6tBw16SYUCkLC8W6YSWmERA2FghCHKKXWDjZiOqmUWj3YtOcH8z6rtf4kgD9tuYiE1IaLAhLiEK31nlLq3wL4BQDLAD6gtf5S4GIR0ggKBSHuuQaz8N//BfCzgctCSGMYeiLEPd8N4HkwCx6eDFwWQhpDoSDEPe8DsAOzEdONwGUhpDEMPRHiEKXU3wTwrNb6nyuljgL4lFLqx7TW45zP/gcAfxHA85RS3wTw01rrJ1suMiFz4TLjhBBCSmHoiRBCSCkMPRHikYP90P9Z5u1vaa3/cojyELIIDD0RQggphaEnQgghpVAoCCGElEKhIIQQUgqFghBCSCn/H0DVsI4GceMzAAAAAElFTkSuQmCC\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('x_1')\n",
    "plt.ylabel('y')\n",
    "plt.plot(x_train[:,-1], y_train, 'bx', linewidth=2)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% code\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Implement locally weighted linear regression:"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "outputs": [],
   "source": [
    "class LocallyWeightedLinearRegression(LinearModel):\n",
    "    \"\"\"Locally Weighted Regression (LWR).\n",
    "\n",
    "    Example usage:\n",
    "        > clf = LocallyWeightedLinearRegression(tau)\n",
    "        > clf.fit(x_train, y_train)\n",
    "        > clf.predict(x_eval)\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, tau):\n",
    "        super(LocallyWeightedLinearRegression, self).__init__()\n",
    "        self.tau = tau\n",
    "        self.x = None\n",
    "        self.y = None\n",
    "\n",
    "    def fit(self, x, y):\n",
    "        \"\"\"Fit LWR by saving the training set.\n",
    "\n",
    "        :param x: Training example inputs. Shape (m, n).\n",
    "        :param y: Training example labels. Shape (m,).\n",
    "        \"\"\"\n",
    "\n",
    "        self.x = x\n",
    "        self.y = y\n",
    "\n",
    "    def predict(self, x):\n",
    "        \"\"\"Make predictions given inputs x.\n",
    "\n",
    "        :param x: Inputs of shape (l, n).\n",
    "        :return:  Outputs of shape (l,).\n",
    "        \"\"\"\n",
    "\n",
    "        l, n = x.shape\n",
    "\n",
    "        # Reshape the input x by adding an additional dimension so that it can broadcast\n",
    "        w_vector = np.exp(- np.linalg.norm(self.x - np.reshape(x, (l, -1, n)), ord=2, axis=2)**2 / (2 * self.tau**2))\n",
    "\n",
    "        # Turn the weights into diagonal matrices, each corresponds to a single input. Shape (l, m, m)\n",
    "        w = np.apply_along_axis(np.diag, axis=1, arr=w_vector)\n",
    "\n",
    "        # Compute theta for each input x^(i). Shape (l, n)\n",
    "        theta = np.linalg.inv(self.x.T @ w @ self.x) @ self.x.T @ w @ self.y\n",
    "\n",
    "        return np.einsum('ij,ij->i', x, theta)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% code\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Train the model:"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "outputs": [],
   "source": [
    "clf = LocallyWeightedLinearRegression(tau=0.5)\n",
    "clf.fit(x_train, y_train)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% code\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Plot predictions on training set and validation set:"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "outputs": [],
   "source": [
    "def plot(x, y_label, y_pred, title):\n",
    "    plt.figure()\n",
    "    plt.plot(x[:,-1], y_label, 'bx', label='label')\n",
    "    plt.plot(x[:,-1], y_pred, 'ro', label='prediction')\n",
    "    plt.suptitle(title, fontsize=12)\n",
    "    plt.legend(loc='upper left')"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% code\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
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      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_train_pred = clf.predict(x_train)\n",
    "plot(x_train, y_train, y_train_pred, 'Training Set')\n",
    "\n",
    "y_valid_pred = clf.predict(x_valid)\n",
    "plot(x_valid, y_valid, y_valid_pred, 'Validation Set')"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% code\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "From the figures, we can see the model is underfitting."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### (c)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "source": [
    "taus = [3e-2, 5e-2, 1e-1, 5e-1, 1e0, 1e1]\n",
    "\n",
    "lowest_mse = math.inf\n",
    "best_tau = taus[0]\n",
    "\n",
    "for tau in taus:\n",
    "    clf = LocallyWeightedLinearRegression(tau)\n",
    "    clf.fit(x_train, y_train)\n",
    "    y_valid_pred = clf.predict(x_valid)\n",
    "\n",
    "    mse = np.mean((y_valid_pred - y_valid)**2)\n",
    "    if mse < lowest_mse:\n",
    "        lowest_mse = mse\n",
    "        best_tau = tau\n",
    "\n",
    "    plot(x_valid, y_valid, y_valid_pred, f'Validation Set (Tau = {tau}, MSE = {mse})')\n",
    "\n",
    "print(f'Tau = {best_tau} achieves the lowest MSE on the validation set.')"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% code\n"
    }
   },
   "execution_count": 17,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tau = 0.05 achieves the lowest MSE on the validation set.\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "Use $\\tau = 0.05$ to make predictions on test set:"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "clf = LocallyWeightedLinearRegression(tau=0.05)\n",
    "clf.fit(x_train, y_train)\n",
    "y_test_pred = clf.predict(x_test)\n",
    "\n",
    "plot(x_test, y_test, y_test_pred, f'Test Set (MSE = {np.mean((y_test_pred - y_test)**2)})')"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% code\n"
    }
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "name": "cs229",
   "language": "python",
   "display_name": "cs229"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}